Applying suction on at least part of the surface of an object has been used to reduce drag. This can delay or prevent flow separation and also reduce the wall shear stress. This problem focuses on the latter effect. Suppose that suction on a porous flat plate creates a velocity normal to its surface that is given by v_y(x, 0) = −v₀, where v₀ is a positive constant. The no-slip condition continues to apply. It may be assumed that v₀⁄U is small enough that the boundary-layer approximation is still valid and that the outer velocity (U) remains nearly constant.

(a) The flow in the boundary layer eventually becomes fully developed. Determine v_x(y) and the wall shear stress in that region. (You should find that τ₀ is independent of μ there!)

(b) If the flow over nearly the entire length L of a plate of width W were like that in part (a), how would the drag compare with that in the absence of suction?